Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality

Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with K_ε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.     

Radical copolymerization of 2-acryloyl thioxanthone with methyl methacrylate

A novel monomer, 2-acryloyl thioxanthone (TXA), was prepared by reaction of 2-hydroxy thioxanthone with acryloyl chloride. Copolymerization of TXA with methyl methacrylate (MMA) in DMF at 80°C was studied in order to evaluate relative reactivities of these monomers. Values of 1.36 and 0.5 were found for the respective reactivity ratios of MMA and TXA, respectively. The resonance stabilization and polar properties were determined and discussed in terms of spectroscopic data.     

Graph bisection algorithms with good average case behavior

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n ^{1?1/[(d+1)/2]}), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n ^2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:

1. the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
2. whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
3. the algorithm works well both theoretically and experimentally,
4. the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
5. the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).

     

1,4-Addition of benzene to a dihydrocyclopent[a]indene diradical: synthesis and DFT study

Photochemical cyclization of compound 1, a homoenediyne (-CCC=CCH2CC-) bearing two ethynylanthracene chromophores, yields two isomeric dihydrocyclopent[a]indene ring systems, spiro-fused to the 9-position of a 9,10-dihydroanthracene moiety. Evidence of a photochemically initiated diradical cyclization pathway is proposed on the basis of (i) hydrogen abstraction from reaction with 1,4-cyclohexadiene (1,4-CHD) and (ii) the observation of 1,4-addition of benzene (solvent). The reaction was further analyzed by a complete density functional theory (DFT) study, using an unrestricted approach (UBLYP) with a 6-31G* basis set for the open-shell triplet states of the reactants, products, and diradical intermediates to model the photochemical nature of observed transformation. A mechanism detailing the observed cyclization/addition reaction is proposed.     

Benzo[d]-1,2-oxaphospholes as precursors of stabilized C-centered radicals

[reaction: see text] Several benzo[d]-1,2-oxaphosphole 2-oxides were examined as potential precursors of stabilized C-centered radicals. The transient absorption spectra obtained after laser flash photolysis in the presence of di-tert-butyl peroxide showed the features of benzylic radicals with formation and decay kinetics not significantly influenced by the presence of oxygen. In the case of compounds with two possible diastereomeric forms, the C-H bond of the trans-isomers [corrected] is more reactive toward hydrogen abstraction.     

Physicochemical and structural properties of bacteriostatic sulfonamides: Theoretical study

A theoretical study at the Hartree–Fock and density functional theory levels is performed on sulfonamide‐type bacteriostatic compounds with the aim to provide an insight into their structure–activity relationship. The basicity of the p‐amino group is analyzed by means of the proton affinities and the protonation energies, showing that molecules presenting bacteriostatic activity are less basic, i.e., they are characterized by larger protonation energies and smaller proton affinities. The acidity of the amide group is analyzed through the deprotonation energy. The results reveal that the more acidic molecules present a larger bacteriostatic activity. This result is also confirmed from a study of bond orders. A bond order analysis of the amide group suggests that the electron attracting group in these molecules is responsible for the increase in acidity. The charge of the SO₂ group is also shown to be affected by the presence of the electron attracting group and consequently related to the acidity of the molecules. A geometric analysis shows that structures in which the amino group is more coplanar with respect to the benzenic ring possess larger bacteriostatic activity. A conformational analysis of these molecules illustrates that active molecules have relatively larger torsion energy barriers. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 165–172, 2003     

Kinetic parameters of unsaturated polyester resin modified with poly(ε -caprolactone)

The mineral sabugalite (HAl)_0.5[(UO₂)₂(PO₄)]₂⋅8H₂O, has been studied using a combination of energy dispersive X-ray analysis, X-ray diffraction, dynamic and controlled rate thermal analysis techniques. X-ray diffraction shows that the starting material in the thermal decomposition is sabugalite and the product of the thermal treatment is a mixture of aluminium and uranyl phosphates. Four mass loss steps are observed for the dehydration of sabugalite at 48°C (temperature range 39 to 59°C), 84°C (temperature range 59 to 109°C), 127°C (temperature range 109 to 165°C) and around 270°C (temperature range 175 to 525°C) with mass losses of 2.8, 6.5, 2.3 and 4.4%, respectively, making a total mass loss of water of 16.0%. In the CRTA experiment mass loss stages were found at 60, 97, 140 and 270°C which correspond to four dehydration steps involving the loss of 2, 6, 6 and 2 moles of water. These mass losses result in the formation of four phases namely meta(I)sabugalite, meta(II)sabugalite, meta(III)sabugalite and finally uranyl phosphate and alumina phosphates. The use of a combination of dynamic and controlled rate thermal analysis techniques enabled a definitive study of the thermal decomposition of sabugalite. While the temperature ranges and the mass losses vary due to the different experimental conditions, the results of the CRTA analysis should be considered as standard data due to the quasi-equilibrium nature of the thermal decomposition process. The online version of the original article can be found at     

Cure kinetics of epoxy resin and thermoplastic polymer

The cure kinetics and morphology of diglycidyl ether of bisphenol A (DGEBA) modified with polyvinyl acetate (PVAc) using diaminodiphenylmethane (DDM) as hardener were investigated through differential scanning calorimetry (DSC) and environmental scanning electron microscopy (ESEM). Isothermal curing measurements were carried out at 150, 120 and 80°C. The kinetic parameters were obtained using the general autocatalytic chemically controlled model. The comparison of the kinetic data indicates that the presence of PVAc does not change the autocatalytic nature of the cure reaction. Two T _g’s were observed in the fully cured samples of the modified systems. ESEM micrographies confirm the biphasic morphology.